Question

if you are given the graph of (g(x) = log_{2}x), how could you graph (f(x) = log_{2}x + 5)?

translate each point of the graph of (g(x)) 5 units up.
translate each point of the graph of (g(x)) 5 units down.
translate each point of the graph of (g(x)) 5 units left.
translate each point of the graph of (g(x)) 5 units right.

Explanation:

Identify the relationship between the functions

Using the Logarithmic Function Transformations knowledge point

$$ f(x) = g(x) + 5 $$

Determine the geometric transformation

Using the Vertical Translation knowledge point

$$ y \to y + k \quad (k = 5 > 0) $$

This represents a vertical shift of 5 units upward.

Answer:

• Translate each point of the graph of \(g(x)\) 5 units up. (Correct answer)
• Translate each point of the graph of \(g(x)\) 5 units down.
• Translate each point of the graph of \(g(x)\) 5 units left.
• Translate each point of the graph of \(g(x)\) 5 units right.